Time-oscillating Lyapunov modes and auto-correlation functions for quasi-one-dimensional systems

The time-dependent structure of the Lyapunov vectors corresponding to the steps of Lyapunov spectra and their basis set representation are discussed for a quasi-one-dimensional many-hard-disk systems. Time-oscillating behavior is observed in two types of Lyapunov modes, one associated with the time translational invariance and another with the spatial translational invariance, and their phase relation is specified. It is shown that the longest period of the Lyapunov modes is twice as long as the period of the longitudinal momentum auto-correlation function. A simple explanation for this relation is proposed. This result gives the first quantitative connection between the Lyapunov modes and an experimentally accessible quantity.Comment: 4 pages, 3 figure

Hopping dynamics for localized Lyapunov vectors in many-hard-disk systems

The dynamics of the localized region of the Lyapunov vector for the largest Lyapunov exponent is discussed in quasi-one-dimensional hard-disk systems at low density. We introduce a hopping rate to quantitatively describe the movement of the localized region of this Lyapunov vector, and show that it is a decreasing function of hopping distance, implying spatial correlation of the localized regions. This behavior is explained quantitatively by a brick accumulation model derived from hard-disk dynamics in the low density limit, in which hopping of the localized Lyapunov vector is represented as the movement of the highest brick position. We also give an analytical expression for the hopping rate, which is obtained us a sum of probability distributions for brick height configurations between two separated highest brick sites. The results of these simple models are in good agreement with the simulation results for hard-disk systems.Comment: 28 pages, 13 figure

Bootleggers, Baptists &(and) Televangelists: Regulating Tobacco by Litigation

The bootleggers and Baptists public choice theory of regulation explains how durable regulatory bargains can arise from the tacit collaboration of a public-interest-minded interest group (the Baptists) with an economic interest (the bootleggers). Using the history of tobacco regulation, this Article extends the bootleggers and Baptists theory of regulation to incorporate the role of policy entrepreneurs like the state attorneys general and private trial lawyers who joined forces to regulate tobacco by litigation. We denominate these actors televangelists and demonstrate that they play a pernicious role in regulation. The Article begins by showing how tobacco regulation through the 1980s fit the traditional bootleggers and Baptists public choice model. It then explores the circumstances that made it possible for the emergence of the televangelists as a regulatory partner that the bootleggers would prefer. The Article then criticizes televangelist-bootlegger bargains as likely to result in substantial wealth transfers from large, unorganized groups to the coalition partners. It also shows how televangelist-bootlegger coalitions are more pernicious than bootlegger-Baptist coalitions. Finally, it concludes with suggestions for how to make televangelist-bootlegger coalitions less durable

Microscopic expressions for the thermodynamic temperature

We show that arbitrary phase space vector fields can be used to generate phase functions whose ensemble averages give the thermodynamic temperature. We describe conditions for the validity of these functions in periodic boundary systems and the Molecular Dynamics (MD) ensemble, and test them with a short-ranged potential MD simulation.Comment: 21 pages, 2 figures, Revtex. Submitted to Phys. Rev.

Time-dependent mode structure for Lyapunov vectors as a collective movement in quasi-one-dimensional systems

Time dependent mode structure for the Lyapunov vectors associated with the stepwise structure of the Lyapunov spectra and its relation to the momentum auto-correlation function are discussed in quasi-one-dimensional many-hard-disk systems. We demonstrate mode structures (Lyapunov modes) for all components of the Lyapunov vectors, which include the longitudinal and transverse components of their spatial and momentum parts, and their phase relations are specified. These mode structures are suggested from the form of the Lyapunov vectors corresponding to the zero-Lyapunov exponents. Spatial node structures of these modes are explained by the reflection properties of the hard-walls used in the models. Our main interest is the time-oscillating behavior of Lyapunov modes. It is shown that the largest time-oscillating period of the Lyapunov modes is twice as long as the time-oscillating period of the longitudinal momentum auto-correlation function. This relation is satisfied irrespective of the particle number and boundary conditions. A simple explanation for this relation is given based on the form of the Lyapunov vector.Comment: 39 pages, 21 figures, Manuscript including the figures of better quality is available from http://www.phys.unsw.edu.au/~gary/Research.htm

From Lyapunov modes to the exponents for hard disk systems

We demonstrate the preservation of the Lyapunov modes by the underlying tangent space dynamics of hard disks. This result is exact for the zero modes and correct to order $\epsilon$ for the transverse and LP modes where $\epsilon$ is linear in the mode number. For sufficiently large mode numbers the dynamics no longer preserves the mode structure. We propose a Gram-Schmidt procedure based on orthogonality with respect to the centre space that determines the values of the Lyapunov exponents for the modes. This assumes a detailed knowledge of the modes, but from that predicts the values of the exponents from the modes. Thus the modes and the exponents contain the same information

Lyapunov instability for a periodic Lorentz gas thermostated by deterministic scattering

In recent work a deterministic and time-reversible boundary thermostat called thermostating by deterministic scattering has been introduced for the periodic Lorentz gas [Phys. Rev. Lett. {\bf 84}, 4268 (2000)]. Here we assess the nonlinear properties of this new dynamical system by numerically calculating its Lyapunov exponents. Based on a revised method for computing Lyapunov exponents, which employs periodic orthonormalization with a constraint, we present results for the Lyapunov exponents and related quantities in equilibrium and nonequilibrium. Finally, we check whether we obtain the same relations between quantities characterizing the microscopic chaotic dynamics and quantities characterizing macroscopic transport as obtained for conventional deterministic and time-reversible bulk thermostats.Comment: 18 pages (revtex), 7 figures (postscript

What do I do now? Intolerance of uncertainty is associated with discrete patterns of anticipatory physiological responding to different contexts

Heightened physiological responses to uncertainty are a common hallmark of anxiety disorders. Many separate studies have examined the relationship between individual differences in intolerance of uncertainty (IU) and physiological responses to uncertainty during different contexts. Despite this there is a scarcity of research examining the extent to which individual differences in IU are related to shared or discrete patterns of anticipatory physiological responding across different contexts. Anticipatory physiological responses to uncertainty were assessed in three different contexts (associative threat learning and extinction, threat uncertainty, decision-making) within the same sample (n = 45). During these tasks, behavioural responses (i.e. reaction times, choices), skin conductance and corrugator supercilli activity were recorded. In addition, self-reported IU and trait anxiety were measured. IU was related to both skin conductance and corrugator supercilii activity for the associative threat learning and extinction context, and decision-making context. However, trait anxiety was related to corrugator supercilii activity during the threat uncertainty context. Ultimately, this research helps us further tease apart the role of IU on different aspects of anticipation (i.e. valence and arousal) across contexts, which will be relevant for future IU-related models of psychopathology

Integration through transients for Brownian particles under steady shear

Starting from the microscopic Smoluchowski equation for interacting Brownian particles under stationary shearing, exact expressions for shear-dependent steady-state averages, correlation and structure functions, and susceptibilities are obtained, which take the form of generalized Green-Kubo relations. They require integration of transient dynamics. Equations of motion with memory effects for transient density fluctuation functions are derived from the same microscopic starting point. We argue that the derived formal expressions provide useful starting points for approximations in order to describe the stationary non-equilibrium state of steadily sheared dense colloidal dispersions.Comment: 17 pages, Submitted to J. Phys.: Condens. Matter; revised version with minor correction